For the error in the freezing solutions of linear boundary value problems we obtain a bound which is sharper than that obtained recently by Shahruz and Schwartz [Appl. Math. Comput. 60 (1994) 285; Comput. Math. Appl. 28 (1994) 75]. A different freezing technique, 'global freezing', is also proposed. It is shown that this new technique is easy to implement for numerical computation of the solutions. Moreover, the corresponding solution has an error bound similar to that of the freezing method.